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Correlation coefficients play a pivotal role in quantifying linear relationships between random variables. Yet, their application to time series data is very challenging due to temporal dependencies. This paper introduces a novel approach to estimate the statistical significance of correlation coefficients in time series data, addressing the limitations of traditional methods based on the concept of effective degrees of freedom (or effective sample size, ESS). These effective degrees of freedom represent the independent sample size that would yield comparable test statistics under the assumption of no temporal correlation. We propose to assume a parametric Gaussian form for the autocorrelation function. We show that this assumption, motivated by a Laplace approximation, enables a simple estimator of the ESS that depends only on the temporal derivatives of the time series. Through numerical experiments, we show that the proposed approach yields accurate statistics while significantly reducing computational overhead. In addition, we evaluate the adequacy of our approach on real physiological signals, for assessing the connectivity measures in electrophysiology and detecting correlated arm movements in motion capture data. Our methodology provides a simple tool for researchers working with time series data, enabling robust hypothesis testing in the presence of temporal dependencies.

The assessment of regression models with discrete outcomes is challenging and has many fundamental issues. With discrete outcomes, standard regression model assessment tools such as Pearson and deviance residuals do not follow the conventional reference distribution (normal) under the true model, calling into question the legitimacy of model assessment based on these tools. To fill this gap, we construct a new type of residuals for general discrete outcomes, including ordinal and count outcomes. The proposed residuals are based on two layers of probability integral transformation. When at least one continuous covariate is available, the proposed residuals closely follow a uniform distribution (or a normal distribution after transformation) under the correctly specified model. One can construct visualizations such as QQ plots to check the overall fit of a model straightforwardly, and the shape of QQ plots can further help identify possible causes of misspecification such as overdispersion. We provide theoretical justification for the proposed residuals by establishing their asymptotic properties. Moreover, in order to assess the mean structure and identify potential covariates, we develop an ordered curve as a supplementary tool, which is based on the comparison between the partial sum of outcomes and of fitted means. Through simulation, we demonstrate empirically that the proposed tools outperform commonly used residuals for various model assessment tasks. We also illustrate the workflow of model assessment using the proposed tools in data analysis.

Assistive robots should be able to wash, fold or iron clothes. However, due to the variety, deformability and self-occlusions of clothes, creating general-purpose robot systems for cloth manipulation is challenging. Synthetic data is a promising direction to improve generalization, though its usability is often limited by the sim-to-real gap. To advance the use of synthetic data for cloth manipulation and to enable tasks such as robotic folding, we present a synthetic data pipeline to train keypoint detectors for almost flattened cloth items. To test its performance, we have also collected a real-world dataset. We train detectors for both T-shirts, towels and shorts and obtain an average precision of 64.3%. Fine-tuning on real-world data improves performance to 74.2%. Additional insight is provided by discussing various failure modes of the keypoint detectors and by comparing different approaches to obtain cloth meshes and materials. We also quantify the remaining sim-to-real gap and argue that further improvements to the fidelity of cloth assets will be required to further reduce this gap. The code, dataset and trained models are available online.

Neural implicit fields, such as the neural signed distance field (SDF) of a shape, have emerged as a powerful representation for many applications, e.g., encoding a 3D shape and performing collision detection. Typically, implicit fields are encoded by Multi-layer Perceptrons (MLP) with positional encoding (PE) to capture high-frequency geometric details. However, a notable side effect of such PE-equipped MLPs is the noisy artifacts present in the learned implicit fields. While increasing the sampling rate could in general mitigate these artifacts, in this paper we aim to explain this adverse phenomenon through the lens of Fourier analysis. We devise a tool to determine the appropriate sampling rate for learning an accurate neural implicit field without undesirable side effects. Specifically, we propose a simple yet effective method to estimate the intrinsic frequency of a given network with randomized weights based on the Fourier analysis of the network's responses. It is observed that a PE-equipped MLP has an intrinsic frequency much higher than the highest frequency component in the PE layer. Sampling against this intrinsic frequency following the Nyquist-Sannon sampling theorem allows us to determine an appropriate training sampling rate. We empirically show in the setting of SDF fitting that this recommended sampling rate is sufficient to secure accurate fitting results, while further increasing the sampling rate would not further noticeably reduce the fitting error. Training PE-equipped MLPs simply with our sampling strategy leads to performances superior to the existing methods.

Graphs are important data representations for describing objects and their relationships, which appear in a wide diversity of real-world scenarios. As one of a critical problem in this area, graph generation considers learning the distributions of given graphs and generating more novel graphs. Owing to their wide range of applications, generative models for graphs, which have a rich history, however, are traditionally hand-crafted and only capable of modeling a few statistical properties of graphs. Recent advances in deep generative models for graph generation is an important step towards improving the fidelity of generated graphs and paves the way for new kinds of applications. This article provides an extensive overview of the literature in the field of deep generative models for graph generation. Firstly, the formal definition of deep generative models for the graph generation and the preliminary knowledge are provided. Secondly, taxonomies of deep generative models for both unconditional and conditional graph generation are proposed respectively; the existing works of each are compared and analyzed. After that, an overview of the evaluation metrics in this specific domain is provided. Finally, the applications that deep graph generation enables are summarized and five promising future research directions are highlighted.

The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.

Graph Convolutional Networks (GCNs) have been widely applied in various fields due to their significant power on processing graph-structured data. Typical GCN and its variants work under a homophily assumption (i.e., nodes with same class are prone to connect to each other), while ignoring the heterophily which exists in many real-world networks (i.e., nodes with different classes tend to form edges). Existing methods deal with heterophily by mainly aggregating higher-order neighborhoods or combing the immediate representations, which leads to noise and irrelevant information in the result. But these methods did not change the propagation mechanism which works under homophily assumption (that is a fundamental part of GCNs). This makes it difficult to distinguish the representation of nodes from different classes. To address this problem, in this paper we design a novel propagation mechanism, which can automatically change the propagation and aggregation process according to homophily or heterophily between node pairs. To adaptively learn the propagation process, we introduce two measurements of homophily degree between node pairs, which is learned based on topological and attribute information, respectively. Then we incorporate the learnable homophily degree into the graph convolution framework, which is trained in an end-to-end schema, enabling it to go beyond the assumption of homophily. More importantly, we theoretically prove that our model can constrain the similarity of representations between nodes according to their homophily degree. Experiments on seven real-world datasets demonstrate that this new approach outperforms the state-of-the-art methods under heterophily or low homophily, and gains competitive performance under homophily.

Incompleteness is a common problem for existing knowledge graphs (KGs), and the completion of KG which aims to predict links between entities is challenging. Most existing KG completion methods only consider the direct relation between nodes and ignore the relation paths which contain useful information for link prediction. Recently, a few methods take relation paths into consideration but pay less attention to the order of relations in paths which is important for reasoning. In addition, these path-based models always ignore nonlinear contributions of path features for link prediction. To solve these problems, we propose a novel KG completion method named OPTransE. Instead of embedding both entities of a relation into the same latent space as in previous methods, we project the head entity and the tail entity of each relation into different spaces to guarantee the order of relations in the path. Meanwhile, we adopt a pooling strategy to extract nonlinear and complex features of different paths to further improve the performance of link prediction. Experimental results on two benchmark datasets show that the proposed model OPTransE performs better than state-of-the-art methods.

Image segmentation is still an open problem especially when intensities of the interested objects are overlapped due to the presence of intensity inhomogeneity (also known as bias field). To segment images with intensity inhomogeneities, a bias correction embedded level set model is proposed where Inhomogeneities are Estimated by Orthogonal Primary Functions (IEOPF). In the proposed model, the smoothly varying bias is estimated by a linear combination of a given set of orthogonal primary functions. An inhomogeneous intensity clustering energy is then defined and membership functions of the clusters described by the level set function are introduced to rewrite the energy as a data term of the proposed model. Similar to popular level set methods, a regularization term and an arc length term are also included to regularize and smooth the level set function, respectively. The proposed model is then extended to multichannel and multiphase patterns to segment colourful images and images with multiple objects, respectively. It has been extensively tested on both synthetic and real images that are widely used in the literature and public BrainWeb and IBSR datasets. Experimental results and comparison with state-of-the-art methods demonstrate that advantages of the proposed model in terms of bias correction and segmentation accuracy.

Recommender System (RS) is a hot area where artificial intelligence (AI) techniques can be effectively applied to improve performance. Since the well-known Netflix Challenge, collaborative filtering (CF) has become the most popular and effective recommendation method. Despite their success in CF, various AI techniques still have to face the data sparsity and cold start problems. Previous works tried to solve these two problems by utilizing auxiliary information, such as social connections among users and meta-data of items. However, they process different types of information separately, leading to information loss. In this work, we propose to utilize Heterogeneous Information Network (HIN), which is a natural and general representation of different types of data, to enhance CF-based recommending methods. HIN-based recommender systems face two problems: how to represent high-level semantics for recommendation and how to fuse the heterogeneous information to recommend. To address these problems, we propose to applying meta-graph to HIN-based RS and solve the information fusion problem with a "matrix factorization (MF) + factorization machine (FM)" framework. For the "MF" part, we obtain user-item similarity matrices from each meta-graph and adopt low-rank matrix approximation to get latent features for both users and items. For the "FM" part, we propose to apply FM with Group lasso (FMG) on the obtained features to simultaneously predict missing ratings and select useful meta-graphs. Experimental results on two large real-world datasets, i.e., Amazon and Yelp, show that our proposed approach is better than that of the state-of-the-art FM and other HIN-based recommending methods.